Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.5 | ||
Root | \(5.44232i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.4.c.f.99.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 6.44232i | 1.23983i | 0.784671 | + | 0.619913i | \(0.212832\pi\) | ||||
−0.784671 | + | 0.619913i | \(0.787168\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −6.24768 | + | 9.27181i | −0.558810 | + | 0.829296i | ||||
\(6\) | 12.8846 | 0.876689 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −14.5035 | −0.537168 | ||||||||
\(10\) | 18.5436 | + | 12.4954i | 0.586401 | + | 0.395138i | ||||
\(11\) | 48.3846 | 1.32623 | 0.663114 | − | 0.748518i | \(-0.269234\pi\) | ||||
0.663114 | + | 0.748518i | \(0.269234\pi\) | |||||||
\(12\) | − | 25.7693i | − | 0.619913i | ||||||
\(13\) | 93.4871i | 1.99451i | 0.0740250 | + | 0.997256i | \(0.476416\pi\) | ||||
−0.0740250 | + | 0.997256i | \(0.523584\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −59.7320 | − | 40.2496i | −1.02818 | − | 0.692827i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 20.2793i | 0.289320i | 0.989481 | + | 0.144660i | \(0.0462089\pi\) | ||||
−0.989481 | + | 0.144660i | \(0.953791\pi\) | |||||||
\(18\) | 29.0071i | 0.379835i | ||||||||
\(19\) | 31.0581 | 0.375011 | 0.187506 | − | 0.982264i | \(-0.439960\pi\) | ||||
0.187506 | + | 0.982264i | \(0.439960\pi\) | |||||||
\(20\) | 24.9907 | − | 37.0872i | 0.279405 | − | 0.414648i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 96.7692i | − | 0.937785i | ||||||
\(23\) | 21.0487i | 0.190825i | 0.995438 | + | 0.0954123i | \(0.0304170\pi\) | ||||
−0.995438 | + | 0.0954123i | \(0.969583\pi\) | |||||||
\(24\) | −51.5386 | −0.438345 | ||||||||
\(25\) | −46.9329 | − | 115.855i | −0.375463 | − | 0.926837i | ||||
\(26\) | 186.974 | 1.41033 | ||||||||
\(27\) | 80.5063i | 0.573831i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −69.5116 | −0.445103 | −0.222551 | − | 0.974921i | \(-0.571438\pi\) | ||||
−0.222551 | + | 0.974921i | \(0.571438\pi\) | |||||||
\(30\) | −80.4992 | + | 119.464i | −0.489902 | + | 0.727035i | ||||
\(31\) | 161.116 | 0.933462 | 0.466731 | − | 0.884399i | \(-0.345432\pi\) | ||||
0.466731 | + | 0.884399i | \(0.345432\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | 311.709i | 1.64429i | ||||||||
\(34\) | 40.5585 | 0.204580 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 58.0141 | 0.268584 | ||||||||
\(37\) | 162.582i | 0.722386i | 0.932491 | + | 0.361193i | \(0.117630\pi\) | ||||
−0.932491 | + | 0.361193i | \(0.882370\pi\) | |||||||
\(38\) | − | 62.1162i | − | 0.265173i | ||||||
\(39\) | −602.274 | −2.47285 | ||||||||
\(40\) | −74.1745 | − | 49.9815i | −0.293200 | − | 0.197569i | ||||
\(41\) | −365.073 | −1.39060 | −0.695302 | − | 0.718717i | \(-0.744730\pi\) | ||||
−0.695302 | + | 0.718717i | \(0.744730\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 254.518i | − | 0.902644i | −0.892361 | − | 0.451322i | \(-0.850953\pi\) | ||
0.892361 | − | 0.451322i | \(-0.149047\pi\) | |||||||
\(44\) | −193.538 | −0.663114 | ||||||||
\(45\) | 90.6134 | − | 134.474i | 0.300175 | − | 0.445471i | ||||
\(46\) | 42.0975 | 0.134933 | ||||||||
\(47\) | − | 468.802i | − | 1.45493i | −0.686144 | − | 0.727466i | \(-0.740698\pi\) | ||
0.686144 | − | 0.727466i | \(-0.259302\pi\) | |||||||
\(48\) | 103.077i | 0.309956i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −231.709 | + | 93.8658i | −0.655373 | + | 0.265493i | ||||
\(51\) | −130.646 | −0.358707 | ||||||||
\(52\) | − | 373.949i | − | 0.997256i | ||||||
\(53\) | 587.150i | 1.52172i | 0.648915 | + | 0.760861i | \(0.275223\pi\) | ||||
−0.648915 | + | 0.760861i | \(0.724777\pi\) | |||||||
\(54\) | 161.013 | 0.405760 | ||||||||
\(55\) | −302.292 | + | 448.613i | −0.741109 | + | 1.09984i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 200.086i | 0.464949i | ||||||||
\(58\) | 139.023i | 0.314735i | ||||||||
\(59\) | −536.945 | −1.18482 | −0.592409 | − | 0.805637i | \(-0.701823\pi\) | ||||
−0.592409 | + | 0.805637i | \(0.701823\pi\) | |||||||
\(60\) | 238.928 | + | 160.998i | 0.514091 | + | 0.346413i | ||||
\(61\) | −625.824 | −1.31358 | −0.656791 | − | 0.754072i | \(-0.728087\pi\) | ||||
−0.656791 | + | 0.754072i | \(0.728087\pi\) | |||||||
\(62\) | − | 322.232i | − | 0.660057i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −866.795 | − | 584.078i | −1.65404 | − | 1.11455i | ||||
\(66\) | 623.419 | 1.16269 | ||||||||
\(67\) | − | 123.074i | − | 0.224416i | −0.993685 | − | 0.112208i | \(-0.964208\pi\) | ||
0.993685 | − | 0.112208i | \(-0.0357922\pi\) | |||||||
\(68\) | − | 81.1171i | − | 0.144660i | ||||||
\(69\) | −135.603 | −0.236589 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 210.060 | 0.351121 | 0.175560 | − | 0.984469i | \(-0.443826\pi\) | ||||
0.175560 | + | 0.984469i | \(0.443826\pi\) | |||||||
\(72\) | − | 116.028i | − | 0.189917i | ||||||
\(73\) | − | 141.783i | − | 0.227322i | −0.993520 | − | 0.113661i | \(-0.963742\pi\) | ||
0.993520 | − | 0.113661i | \(-0.0362578\pi\) | |||||||
\(74\) | 325.164 | 0.510804 | ||||||||
\(75\) | 746.373 | − | 302.357i | 1.14912 | − | 0.465509i | ||||
\(76\) | −124.232 | −0.187506 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1204.55i | 1.74857i | ||||||||
\(79\) | −513.424 | −0.731198 | −0.365599 | − | 0.930772i | \(-0.619136\pi\) | ||||
−0.365599 | + | 0.930772i | \(0.619136\pi\) | |||||||
\(80\) | −99.9629 | + | 148.349i | −0.139702 | + | 0.207324i | ||||
\(81\) | −910.243 | −1.24862 | ||||||||
\(82\) | 730.146i | 0.983306i | ||||||||
\(83\) | − | 117.376i | − | 0.155225i | −0.996984 | − | 0.0776125i | \(-0.975270\pi\) | ||
0.996984 | − | 0.0776125i | \(-0.0247297\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −188.025 | − | 126.698i | −0.239932 | − | 0.161675i | ||||
\(86\) | −509.037 | −0.638266 | ||||||||
\(87\) | − | 447.816i | − | 0.551850i | ||||||
\(88\) | 387.077i | 0.468892i | ||||||||
\(89\) | 61.2589 | 0.0729598 | 0.0364799 | − | 0.999334i | \(-0.488386\pi\) | ||||
0.0364799 | + | 0.999334i | \(0.488386\pi\) | |||||||
\(90\) | −268.948 | − | 181.227i | −0.314996 | − | 0.212255i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 84.1950i | − | 0.0954123i | ||||||
\(93\) | 1037.96i | 1.15733i | ||||||||
\(94\) | −937.604 | −1.02879 | ||||||||
\(95\) | −194.041 | + | 287.965i | −0.209560 | + | 0.310995i | ||||
\(96\) | 206.154 | 0.219172 | ||||||||
\(97\) | 436.654i | 0.457067i | 0.973536 | + | 0.228533i | \(0.0733930\pi\) | ||||
−0.973536 | + | 0.228533i | \(0.926607\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −701.748 | −0.712407 | ||||||||
\(100\) | 187.732 | + | 463.419i | 0.187732 | + | 0.463419i | ||||
\(101\) | 1768.21 | 1.74201 | 0.871007 | − | 0.491271i | \(-0.163468\pi\) | ||||
0.871007 | + | 0.491271i | \(0.163468\pi\) | |||||||
\(102\) | 261.291i | 0.253644i | ||||||||
\(103\) | − | 849.407i | − | 0.812568i | −0.913747 | − | 0.406284i | \(-0.866824\pi\) | ||
0.913747 | − | 0.406284i | \(-0.133176\pi\) | |||||||
\(104\) | −747.897 | −0.705167 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1174.30 | 1.07602 | ||||||||
\(107\) | 1282.58i | 1.15880i | 0.815044 | + | 0.579399i | \(0.196713\pi\) | ||||
−0.815044 | + | 0.579399i | \(0.803287\pi\) | |||||||
\(108\) | − | 322.025i | − | 0.286916i | ||||||
\(109\) | 598.398 | 0.525836 | 0.262918 | − | 0.964818i | \(-0.415315\pi\) | ||||
0.262918 | + | 0.964818i | \(0.415315\pi\) | |||||||
\(110\) | 897.226 | + | 604.583i | 0.777701 | + | 0.524043i | ||||
\(111\) | −1047.40 | −0.895633 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 860.218i | − | 0.716128i | −0.933697 | − | 0.358064i | \(-0.883437\pi\) | ||
0.933697 | − | 0.358064i | \(-0.116563\pi\) | |||||||
\(114\) | 400.172 | 0.328768 | ||||||||
\(115\) | −195.160 | − | 131.506i | −0.158250 | − | 0.106635i | ||||
\(116\) | 278.046 | 0.222551 | ||||||||
\(117\) | − | 1355.89i | − | 1.07139i | ||||||
\(118\) | 1073.89i | 0.837793i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 321.997 | − | 477.856i | 0.244951 | − | 0.363517i | ||||
\(121\) | 1010.07 | 0.758881 | ||||||||
\(122\) | 1251.65i | 0.928843i | ||||||||
\(123\) | − | 2351.92i | − | 1.72411i | ||||||
\(124\) | −644.465 | −0.466731 | ||||||||
\(125\) | 1367.40 | + | 288.670i | 0.978435 | + | 0.206555i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 971.435i | 0.678748i | 0.940652 | + | 0.339374i | \(0.110215\pi\) | ||||
−0.940652 | + | 0.339374i | \(0.889785\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | 1639.69 | 1.11912 | ||||||||
\(130\) | −1168.16 | + | 1733.59i | −0.788108 | + | 1.16958i | ||||
\(131\) | 149.593 | 0.0997713 | 0.0498856 | − | 0.998755i | \(-0.484114\pi\) | ||||
0.0498856 | + | 0.998755i | \(0.484114\pi\) | |||||||
\(132\) | − | 1246.84i | − | 0.822146i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −246.147 | −0.158686 | ||||||||
\(135\) | −746.439 | − | 502.978i | −0.475876 | − | 0.320663i | ||||
\(136\) | −162.234 | −0.102290 | ||||||||
\(137\) | − | 495.245i | − | 0.308844i | −0.988005 | − | 0.154422i | \(-0.950648\pi\) | ||
0.988005 | − | 0.154422i | \(-0.0493516\pi\) | |||||||
\(138\) | 271.206i | 0.167294i | ||||||||
\(139\) | 466.520 | 0.284674 | 0.142337 | − | 0.989818i | \(-0.454538\pi\) | ||||
0.142337 | + | 0.989818i | \(0.454538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3020.17 | 1.80386 | ||||||||
\(142\) | − | 420.121i | − | 0.248280i | ||||||
\(143\) | 4523.34i | 2.64518i | ||||||||
\(144\) | −232.056 | −0.134292 | ||||||||
\(145\) | 434.286 | − | 644.498i | 0.248728 | − | 0.369122i | ||||
\(146\) | −283.567 | −0.160741 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 650.327i | − | 0.361193i | ||||||
\(149\) | 178.554 | 0.0981723 | 0.0490862 | − | 0.998795i | \(-0.484369\pi\) | ||||
0.0490862 | + | 0.998795i | \(0.484369\pi\) | |||||||
\(150\) | −604.714 | − | 1492.75i | −0.329165 | − | 0.812548i | ||||
\(151\) | 831.668 | 0.448213 | 0.224107 | − | 0.974565i | \(-0.428054\pi\) | ||||
0.224107 | + | 0.974565i | \(0.428054\pi\) | |||||||
\(152\) | 248.465i | 0.132587i | ||||||||
\(153\) | − | 294.121i | − | 0.155413i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1006.60 | + | 1493.84i | −0.521628 | + | 0.774116i | ||||
\(156\) | 2409.10 | 1.23642 | ||||||||
\(157\) | − | 167.697i | − | 0.0852462i | −0.999091 | − | 0.0426231i | \(-0.986429\pi\) | ||
0.999091 | − | 0.0426231i | \(-0.0135715\pi\) | |||||||
\(158\) | 1026.85i | 0.517035i | ||||||||
\(159\) | −3782.61 | −1.88667 | ||||||||
\(160\) | 296.698 | + | 199.926i | 0.146600 | + | 0.0987845i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1820.49i | 0.882907i | ||||||||
\(163\) | 1612.09i | 0.774655i | 0.921942 | + | 0.387327i | \(0.126602\pi\) | ||||
−0.921942 | + | 0.387327i | \(0.873398\pi\) | |||||||
\(164\) | 1460.29 | 0.695302 | ||||||||
\(165\) | −2890.11 | − | 1947.46i | −1.36360 | − | 0.918846i | ||||
\(166\) | −234.752 | −0.109761 | ||||||||
\(167\) | 1590.69i | 0.737073i | 0.929613 | + | 0.368536i | \(0.120141\pi\) | ||||
−0.929613 | + | 0.368536i | \(0.879859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6542.84 | −2.97808 | ||||||||
\(170\) | −253.397 | + | 376.051i | −0.114321 | + | 0.169658i | ||||
\(171\) | −450.452 | −0.201444 | ||||||||
\(172\) | 1018.07i | 0.451322i | ||||||||
\(173\) | 1742.41i | 0.765739i | 0.923802 | + | 0.382870i | \(0.125064\pi\) | ||||
−0.923802 | + | 0.382870i | \(0.874936\pi\) | |||||||
\(174\) | −895.632 | −0.390217 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 774.154 | 0.331557 | ||||||||
\(177\) | − | 3459.17i | − | 1.46897i | ||||||
\(178\) | − | 122.518i | − | 0.0515904i | ||||||
\(179\) | 2429.37 | 1.01441 | 0.507205 | − | 0.861825i | \(-0.330679\pi\) | ||||
0.507205 | + | 0.861825i | \(0.330679\pi\) | |||||||
\(180\) | −362.454 | + | 537.896i | −0.150087 | + | 0.222735i | ||||
\(181\) | 2628.61 | 1.07946 | 0.539732 | − | 0.841837i | \(-0.318526\pi\) | ||||
0.539732 | + | 0.841837i | \(0.318526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4031.76i | − | 1.62861i | ||||||
\(184\) | −168.390 | −0.0674667 | ||||||||
\(185\) | −1507.43 | − | 1015.76i | −0.599072 | − | 0.403676i | ||||
\(186\) | 2075.92 | 0.818356 | ||||||||
\(187\) | 981.204i | 0.383705i | ||||||||
\(188\) | 1875.21i | 0.727466i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 575.929 | + | 388.082i | 0.219907 | + | 0.148181i | ||||
\(191\) | 1124.82 | 0.426122 | 0.213061 | − | 0.977039i | \(-0.431657\pi\) | ||||
0.213061 | + | 0.977039i | \(0.431657\pi\) | |||||||
\(192\) | − | 412.309i | − | 0.154978i | ||||||
\(193\) | − | 2216.08i | − | 0.826514i | −0.910615 | − | 0.413257i | \(-0.864391\pi\) | ||
0.910615 | − | 0.413257i | \(-0.135609\pi\) | |||||||
\(194\) | 873.308 | 0.323195 | ||||||||
\(195\) | 3762.82 | − | 5584.17i | 1.38185 | − | 2.05072i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3125.56i | − | 1.13039i | −0.824958 | − | 0.565194i | \(-0.808801\pi\) | ||
0.824958 | − | 0.565194i | \(-0.191199\pi\) | |||||||
\(198\) | 1403.50i | 0.503748i | ||||||||
\(199\) | −4539.34 | −1.61701 | −0.808506 | − | 0.588488i | \(-0.799724\pi\) | ||||
−0.808506 | + | 0.588488i | \(0.799724\pi\) | |||||||
\(200\) | 926.837 | − | 375.463i | 0.327686 | − | 0.132746i | ||||
\(201\) | 792.881 | 0.278236 | ||||||||
\(202\) | − | 3536.42i | − | 1.23179i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 522.582 | 0.179353 | ||||||||
\(205\) | 2280.86 | − | 3384.89i | 0.777084 | − | 1.15322i | ||||
\(206\) | −1698.81 | −0.574573 | ||||||||
\(207\) | − | 305.281i | − | 0.102505i | ||||||
\(208\) | 1495.79i | 0.498628i | ||||||||
\(209\) | 1502.73 | 0.497350 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2520.40 | 0.822331 | 0.411165 | − | 0.911561i | \(-0.365122\pi\) | ||||
0.411165 | + | 0.911561i | \(0.365122\pi\) | |||||||
\(212\) | − | 2348.60i | − | 0.760861i | ||||||
\(213\) | 1353.28i | 0.435329i | ||||||||
\(214\) | 2565.15 | 0.819394 | ||||||||
\(215\) | 2359.85 | + | 1590.15i | 0.748559 | + | 0.504406i | ||||
\(216\) | −644.051 | −0.202880 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 1196.80i | − | 0.371822i | ||||||
\(219\) | 913.415 | 0.281839 | ||||||||
\(220\) | 1209.17 | − | 1794.45i | 0.370555 | − | 0.549918i | ||||
\(221\) | −1895.85 | −0.577053 | ||||||||
\(222\) | 2094.81i | 0.633308i | ||||||||
\(223\) | 5800.58i | 1.74186i | 0.491405 | + | 0.870931i | \(0.336484\pi\) | ||||
−0.491405 | + | 0.870931i | \(0.663516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 680.693 | + | 1680.30i | 0.201687 | + | 0.497867i | ||||
\(226\) | −1720.44 | −0.506379 | ||||||||
\(227\) | − | 6626.47i | − | 1.93751i | −0.248026 | − | 0.968753i | \(-0.579782\pi\) | ||
0.248026 | − | 0.968753i | \(-0.420218\pi\) | |||||||
\(228\) | − | 800.345i | − | 0.232474i | ||||||
\(229\) | −507.845 | −0.146547 | −0.0732736 | − | 0.997312i | \(-0.523345\pi\) | ||||
−0.0732736 | + | 0.997312i | \(0.523345\pi\) | |||||||
\(230\) | −263.012 | + | 390.320i | −0.0754021 | + | 0.111900i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 556.093i | − | 0.157368i | ||||||
\(233\) | − | 6307.82i | − | 1.77356i | −0.462193 | − | 0.886779i | \(-0.652937\pi\) | ||
0.462193 | − | 0.886779i | \(-0.347063\pi\) | |||||||
\(234\) | −2711.79 | −0.757586 | ||||||||
\(235\) | 4346.64 | + | 2928.92i | 1.20657 | + | 0.813030i | ||||
\(236\) | 2147.78 | 0.592409 | ||||||||
\(237\) | − | 3307.64i | − | 0.906559i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4615.12 | 1.24907 | 0.624535 | − | 0.780997i | \(-0.285289\pi\) | ||||
0.624535 | + | 0.780997i | \(0.285289\pi\) | |||||||
\(240\) | −955.712 | − | 643.993i | −0.257046 | − | 0.173207i | ||||
\(241\) | 1550.70 | 0.414480 | 0.207240 | − | 0.978290i | \(-0.433552\pi\) | ||||
0.207240 | + | 0.978290i | \(0.433552\pi\) | |||||||
\(242\) | − | 2020.14i | − | 0.536610i | ||||||
\(243\) | − | 3690.41i | − | 0.974238i | ||||||
\(244\) | 2503.30 | 0.656791 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4703.83 | −1.21913 | ||||||||
\(247\) | 2903.53i | 0.747965i | ||||||||
\(248\) | 1288.93i | 0.330029i | ||||||||
\(249\) | 756.173 | 0.192452 | ||||||||
\(250\) | 577.340 | − | 2734.81i | 0.146057 | − | 0.691858i | ||||
\(251\) | 762.543 | 0.191758 | 0.0958790 | − | 0.995393i | \(-0.469434\pi\) | ||||
0.0958790 | + | 0.995393i | \(0.469434\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1018.44i | 0.253077i | ||||||||
\(254\) | 1942.87 | 0.479947 | ||||||||
\(255\) | 816.232 | − | 1211.32i | 0.200449 | − | 0.297474i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 2302.36i | − | 0.558822i | −0.960172 | − | 0.279411i | \(-0.909861\pi\) | ||
0.960172 | − | 0.279411i | \(-0.0901392\pi\) | |||||||
\(258\) | − | 3279.38i | − | 0.791338i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3467.18 | + | 2336.31i | 0.827021 | + | 0.557277i | ||||
\(261\) | 1008.16 | 0.239095 | ||||||||
\(262\) | − | 299.187i | − | 0.0705490i | ||||||
\(263\) | − | 4833.50i | − | 1.13326i | −0.823974 | − | 0.566628i | \(-0.808248\pi\) | ||
0.823974 | − | 0.566628i | \(-0.191752\pi\) | |||||||
\(264\) | −2493.67 | −0.581345 | ||||||||
\(265\) | −5443.94 | − | 3668.33i | −1.26196 | − | 0.850353i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 394.649i | 0.0904575i | ||||||||
\(268\) | 492.295i | 0.112208i | ||||||||
\(269\) | −4830.35 | −1.09484 | −0.547420 | − | 0.836858i | \(-0.684390\pi\) | ||||
−0.547420 | + | 0.836858i | \(0.684390\pi\) | |||||||
\(270\) | −1005.96 | + | 1492.88i | −0.226743 | + | 0.336495i | ||||
\(271\) | −5950.37 | −1.33380 | −0.666899 | − | 0.745149i | \(-0.732379\pi\) | ||||
−0.666899 | + | 0.745149i | \(0.732379\pi\) | |||||||
\(272\) | 324.468i | 0.0723301i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −990.491 | −0.218386 | ||||||||
\(275\) | −2270.83 | − | 5605.58i | −0.497950 | − | 1.22920i | ||||
\(276\) | 542.411 | 0.118295 | ||||||||
\(277\) | 7668.90i | 1.66346i | 0.555177 | + | 0.831732i | \(0.312651\pi\) | ||||
−0.555177 | + | 0.831732i | \(0.687349\pi\) | |||||||
\(278\) | − | 933.040i | − | 0.201295i | ||||||
\(279\) | −2336.75 | −0.501426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6314.18 | −1.34047 | −0.670235 | − | 0.742149i | \(-0.733807\pi\) | ||||
−0.670235 | + | 0.742149i | \(0.733807\pi\) | |||||||
\(282\) | − | 6040.35i | − | 1.27552i | ||||||
\(283\) | 6122.72i | 1.28607i | 0.765836 | + | 0.643035i | \(0.222325\pi\) | ||||
−0.765836 | + | 0.643035i | \(0.777675\pi\) | |||||||
\(284\) | −840.242 | −0.175560 | ||||||||
\(285\) | −1855.16 | − | 1250.08i | −0.385580 | − | 0.259818i | ||||
\(286\) | 9046.68 | 1.87042 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 464.113i | 0.0949587i | ||||||||
\(289\) | 4501.75 | 0.916294 | ||||||||
\(290\) | −1289.00 | − | 868.573i | −0.261009 | − | 0.175877i | ||||
\(291\) | −2813.07 | −0.566683 | ||||||||
\(292\) | 567.134i | 0.113661i | ||||||||
\(293\) | − | 1646.67i | − | 0.328326i | −0.986433 | − | 0.164163i | \(-0.947508\pi\) | ||
0.986433 | − | 0.164163i | \(-0.0524923\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3354.66 | − | 4978.45i | 0.662088 | − | 0.982564i | ||||
\(296\) | −1300.65 | −0.255402 | ||||||||
\(297\) | 3895.27i | 0.761031i | ||||||||
\(298\) | − | 357.107i | − | 0.0694183i | ||||||
\(299\) | −1967.79 | −0.380602 | ||||||||
\(300\) | −2985.49 | + | 1209.43i | −0.574558 | + | 0.232755i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 1663.34i | − | 0.316934i | ||||||
\(303\) | 11391.4i | 2.15979i | ||||||||
\(304\) | 496.929 | 0.0937528 | ||||||||
\(305\) | 3909.95 | − | 5802.52i | 0.734043 | − | 1.08935i | ||||
\(306\) | −588.242 | −0.109894 | ||||||||
\(307\) | 7890.42i | 1.46687i | 0.679758 | + | 0.733436i | \(0.262085\pi\) | ||||
−0.679758 | + | 0.733436i | \(0.737915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5472.15 | 1.00744 | ||||||||
\(310\) | 2987.68 | + | 2013.21i | 0.547383 | + | 0.368846i | ||||
\(311\) | −3436.98 | −0.626667 | −0.313333 | − | 0.949643i | \(-0.601446\pi\) | ||||
−0.313333 | + | 0.949643i | \(0.601446\pi\) | |||||||
\(312\) | − | 4818.19i | − | 0.874284i | ||||||
\(313\) | 7209.81i | 1.30199i | 0.759082 | + | 0.650995i | \(0.225648\pi\) | ||||
−0.759082 | + | 0.650995i | \(0.774352\pi\) | |||||||
\(314\) | −335.393 | −0.0602782 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2053.69 | 0.365599 | ||||||||
\(317\) | 885.804i | 0.156945i | 0.996916 | + | 0.0784727i | \(0.0250043\pi\) | ||||
−0.996916 | + | 0.0784727i | \(0.974996\pi\) | |||||||
\(318\) | 7565.22i | 1.33408i | ||||||||
\(319\) | −3363.29 | −0.590308 | ||||||||
\(320\) | 399.852 | − | 593.396i | 0.0698512 | − | 0.103662i | ||||
\(321\) | −8262.77 | −1.43671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 629.835i | 0.108498i | ||||||||
\(324\) | 3640.97 | 0.624309 | ||||||||
\(325\) | 10830.9 | − | 4387.62i | 1.84859 | − | 0.748866i | ||||
\(326\) | 3224.18 | 0.547764 | ||||||||
\(327\) | 3855.08i | 0.651945i | ||||||||
\(328\) | − | 2920.58i | − | 0.491653i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3894.92 | + | 5780.22i | −0.649722 | + | 0.964214i | ||||
\(331\) | −1766.18 | −0.293288 | −0.146644 | − | 0.989189i | \(-0.546847\pi\) | ||||
−0.146644 | + | 0.989189i | \(0.546847\pi\) | |||||||
\(332\) | 469.504i | 0.0776125i | ||||||||
\(333\) | − | 2358.01i | − | 0.388042i | ||||||
\(334\) | 3181.38 | 0.521189 | ||||||||
\(335\) | 1141.12 | + | 768.925i | 0.186107 | + | 0.125406i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7521.34i | 1.21577i | 0.794026 | + | 0.607883i | \(0.207981\pi\) | ||||
−0.794026 | + | 0.607883i | \(0.792019\pi\) | |||||||
\(338\) | 13085.7i | 2.10582i | ||||||||
\(339\) | 5541.80 | 0.887874 | ||||||||
\(340\) | 752.102 | + | 506.794i | 0.119966 | + | 0.0808375i | ||||
\(341\) | 7795.54 | 1.23798 | ||||||||
\(342\) | 900.904i | 0.142442i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2036.15 | 0.319133 | ||||||||
\(345\) | 847.203 | − | 1257.28i | 0.132208 | − | 0.196203i | ||||
\(346\) | 3484.82 | 0.541459 | ||||||||
\(347\) | 4658.53i | 0.720700i | 0.932817 | + | 0.360350i | \(0.117343\pi\) | ||||
−0.932817 | + | 0.360350i | \(0.882657\pi\) | |||||||
\(348\) | 1791.26i | 0.275925i | ||||||||
\(349\) | 7198.15 | 1.10403 | 0.552017 | − | 0.833833i | \(-0.313858\pi\) | ||||
0.552017 | + | 0.833833i | \(0.313858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7526.30 | −1.14451 | ||||||||
\(352\) | − | 1548.31i | − | 0.234446i | ||||||
\(353\) | 3640.08i | 0.548844i | 0.961609 | + | 0.274422i | \(0.0884865\pi\) | ||||
−0.961609 | + | 0.274422i | \(0.911514\pi\) | |||||||
\(354\) | −6918.34 | −1.03872 | ||||||||
\(355\) | −1312.39 | + | 1947.64i | −0.196210 | + | 0.291183i | ||||
\(356\) | −245.035 | −0.0364799 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 4858.73i | − | 0.717296i | ||||||
\(359\) | 5469.89 | 0.804150 | 0.402075 | − | 0.915607i | \(-0.368289\pi\) | ||||
0.402075 | + | 0.915607i | \(0.368289\pi\) | |||||||
\(360\) | 1075.79 | + | 724.908i | 0.157498 | + | 0.106128i | ||||
\(361\) | −5894.40 | −0.859367 | ||||||||
\(362\) | − | 5257.22i | − | 0.763296i | ||||||
\(363\) | 6507.20i | 0.940880i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1314.59 | + | 885.818i | 0.188517 | + | 0.127030i | ||||
\(366\) | −8063.52 | −1.15160 | ||||||||
\(367\) | − | 65.0871i | − | 0.00925754i | −0.999989 | − | 0.00462877i | \(-0.998527\pi\) | ||
0.999989 | − | 0.00462877i | \(-0.00147339\pi\) | |||||||
\(368\) | 336.780i | 0.0477062i | ||||||||
\(369\) | 5294.84 | 0.746988 | ||||||||
\(370\) | −2031.52 | + | 3014.85i | −0.285442 | + | 0.423608i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 4151.85i | − | 0.578665i | ||||||
\(373\) | 10153.4i | 1.40944i | 0.709484 | + | 0.704721i | \(0.248928\pi\) | ||||
−0.709484 | + | 0.704721i | \(0.751072\pi\) | |||||||
\(374\) | 1962.41 | 0.271320 | ||||||||
\(375\) | −1859.71 | + | 8809.26i | −0.256093 | + | 1.21309i | ||||
\(376\) | 3750.41 | 0.514396 | ||||||||
\(377\) | − | 6498.44i | − | 0.887763i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1453.96 | −0.197057 | −0.0985287 | − | 0.995134i | \(-0.531414\pi\) | ||||
−0.0985287 | + | 0.995134i | \(0.531414\pi\) | |||||||
\(380\) | 776.164 | − | 1151.86i | 0.104780 | − | 0.155498i | ||||
\(381\) | −6258.30 | −0.841529 | ||||||||
\(382\) | − | 2249.65i | − | 0.301314i | ||||||
\(383\) | − | 577.301i | − | 0.0770201i | −0.999258 | − | 0.0385101i | \(-0.987739\pi\) | ||
0.999258 | − | 0.0385101i | \(-0.0122612\pi\) | |||||||
\(384\) | −824.617 | −0.109586 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4432.16 | −0.584433 | ||||||||
\(387\) | 3691.41i | 0.484871i | ||||||||
\(388\) | − | 1746.62i | − | 0.228533i | ||||||
\(389\) | 2071.00 | 0.269933 | 0.134966 | − | 0.990850i | \(-0.456907\pi\) | ||||
0.134966 | + | 0.990850i | \(0.456907\pi\) | |||||||
\(390\) | −11168.3 | − | 7525.64i | −1.45008 | − | 0.977117i | ||||
\(391\) | −426.853 | −0.0552094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 963.729i | 0.123699i | ||||||||
\(394\) | −6251.11 | −0.799306 | ||||||||
\(395\) | 3207.71 | − | 4760.37i | 0.408601 | − | 0.606380i | ||||
\(396\) | 2806.99 | 0.356203 | ||||||||
\(397\) | − | 5033.42i | − | 0.636322i | −0.948037 | − | 0.318161i | \(-0.896935\pi\) | ||
0.948037 | − | 0.318161i | \(-0.103065\pi\) | |||||||
\(398\) | 9078.68i | 1.14340i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −750.927 | − | 1853.67i | −0.0938658 | − | 0.231709i | ||||
\(401\) | −4946.88 | −0.616048 | −0.308024 | − | 0.951379i | \(-0.599668\pi\) | ||||
−0.308024 | + | 0.951379i | \(0.599668\pi\) | |||||||
\(402\) | − | 1585.76i | − | 0.196743i | ||||||
\(403\) | 15062.3i | 1.86180i | ||||||||
\(404\) | −7072.83 | −0.871007 | ||||||||
\(405\) | 5686.91 | − | 8439.60i | 0.697740 | − | 1.03547i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7866.46i | 0.958049i | ||||||||
\(408\) | − | 1045.16i | − | 0.126822i | ||||||
\(409\) | 9389.84 | 1.13520 | 0.567601 | − | 0.823304i | \(-0.307872\pi\) | ||||
0.567601 | + | 0.823304i | \(0.307872\pi\) | |||||||
\(410\) | −6769.77 | − | 4561.72i | −0.815452 | − | 0.549481i | ||||
\(411\) | 3190.53 | 0.382913 | ||||||||
\(412\) | 3397.63i | 0.406284i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −610.562 | −0.0724819 | ||||||||
\(415\) | 1088.29 | + | 733.327i | 0.128727 | + | 0.0867413i | ||||
\(416\) | 2991.59 | 0.352583 | ||||||||
\(417\) | 3005.47i | 0.352946i | ||||||||
\(418\) | − | 3005.47i | − | 0.351680i | ||||||
\(419\) | −8423.77 | −0.982167 | −0.491084 | − | 0.871112i | \(-0.663399\pi\) | ||||
−0.491084 | + | 0.871112i | \(0.663399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5680.15 | 0.657562 | 0.328781 | − | 0.944406i | \(-0.393362\pi\) | ||||
0.328781 | + | 0.944406i | \(0.393362\pi\) | |||||||
\(422\) | − | 5040.81i | − | 0.581476i | ||||||
\(423\) | 6799.28i | 0.781542i | ||||||||
\(424\) | −4697.20 | −0.538010 | ||||||||
\(425\) | 2349.45 | − | 951.765i | 0.268153 | − | 0.108629i | ||||
\(426\) | 2706.55 | 0.307824 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 5130.31i | − | 0.579399i | ||||||
\(429\) | −29140.8 | −3.27956 | ||||||||
\(430\) | 3180.30 | − | 4719.69i | 0.356669 | − | 0.529311i | ||||
\(431\) | 12348.4 | 1.38005 | 0.690023 | − | 0.723787i | \(-0.257600\pi\) | ||||
0.690023 | + | 0.723787i | \(0.257600\pi\) | |||||||
\(432\) | 1288.10i | 0.143458i | ||||||||
\(433\) | 9031.93i | 1.00242i | 0.865326 | + | 0.501209i | \(0.167111\pi\) | ||||
−0.865326 | + | 0.501209i | \(0.832889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4152.07 | + | 2797.81i | 0.457647 | + | 0.308379i | ||||
\(436\) | −2393.59 | −0.262918 | ||||||||
\(437\) | 653.734i | 0.0715614i | ||||||||
\(438\) | − | 1826.83i | − | 0.199291i | ||||||
\(439\) | 10657.4 | 1.15866 | 0.579329 | − | 0.815094i | \(-0.303315\pi\) | ||||
0.579329 | + | 0.815094i | \(0.303315\pi\) | |||||||
\(440\) | −3588.90 | − | 2418.33i | −0.388851 | − | 0.262022i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3791.70i | 0.408038i | ||||||||
\(443\) | − | 901.320i | − | 0.0966660i | −0.998831 | − | 0.0483330i | \(-0.984609\pi\) | ||
0.998831 | − | 0.0483330i | \(-0.0153909\pi\) | |||||||
\(444\) | 4189.62 | 0.447816 | ||||||||
\(445\) | −382.726 | + | 567.980i | −0.0407707 | + | 0.0605053i | ||||
\(446\) | 11601.2 | 1.23168 | ||||||||
\(447\) | 1150.30i | 0.121717i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7771.88 | 0.816877 | 0.408438 | − | 0.912786i | \(-0.366074\pi\) | ||||
0.408438 | + | 0.912786i | \(0.366074\pi\) | |||||||
\(450\) | 3360.60 | − | 1361.39i | 0.352045 | − | 0.142614i | ||||
\(451\) | −17663.9 | −1.84426 | ||||||||
\(452\) | 3440.87i | 0.358064i | ||||||||
\(453\) | 5357.87i | 0.555706i | ||||||||
\(454\) | −13252.9 | −1.37002 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1600.69 | −0.164384 | ||||||||
\(457\) | − | 2760.35i | − | 0.282547i | −0.989971 | − | 0.141273i | \(-0.954880\pi\) | ||
0.989971 | − | 0.141273i | \(-0.0451196\pi\) | |||||||
\(458\) | 1015.69i | 0.103625i | ||||||||
\(459\) | −1632.61 | −0.166021 | ||||||||
\(460\) | 780.640 | + | 526.024i | 0.0791250 | + | 0.0533173i | ||||
\(461\) | −16482.3 | −1.66520 | −0.832602 | − | 0.553872i | \(-0.813150\pi\) | ||||
−0.832602 | + | 0.553872i | \(0.813150\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9949.16i | 0.998653i | 0.866414 | + | 0.499327i | \(0.166419\pi\) | ||||
−0.866414 | + | 0.499327i | \(0.833581\pi\) | |||||||
\(464\) | −1112.19 | −0.111276 | ||||||||
\(465\) | −9623.79 | − | 6484.86i | −0.959769 | − | 0.646727i | ||||
\(466\) | −12615.6 | −1.25410 | ||||||||
\(467\) | − | 2101.55i | − | 0.208240i | −0.994565 | − | 0.104120i | \(-0.966797\pi\) | ||
0.994565 | − | 0.104120i | \(-0.0332027\pi\) | |||||||
\(468\) | 5423.57i | 0.535694i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5857.85 | − | 8693.28i | 0.574899 | − | 0.853173i | ||||
\(471\) | 1080.36 | 0.105690 | ||||||||
\(472\) | − | 4295.56i | − | 0.418896i | ||||||
\(473\) | − | 12314.8i | − | 1.19711i | ||||||
\(474\) | −6615.28 | −0.641034 | ||||||||
\(475\) | −1457.65 | − | 3598.22i | −0.140803 | − | 0.347574i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 8515.74i | − | 0.817420i | ||||||
\(478\) | − | 9230.25i | − | 0.883225i | ||||||
\(479\) | 8009.97 | 0.764060 | 0.382030 | − | 0.924150i | \(-0.375225\pi\) | ||||
0.382030 | + | 0.924150i | \(0.375225\pi\) | |||||||
\(480\) | −1287.99 | + | 1911.42i | −0.122476 | + | 0.181759i | ||||
\(481\) | −15199.3 | −1.44081 | ||||||||
\(482\) | − | 3101.41i | − | 0.293082i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4040.28 | −0.379441 | ||||||||
\(485\) | −4048.57 | − | 2728.08i | −0.379044 | − | 0.255413i | ||||
\(486\) | −7380.82 | −0.688890 | ||||||||
\(487\) | − | 5382.59i | − | 0.500839i | −0.968137 | − | 0.250420i | \(-0.919431\pi\) | ||
0.968137 | − | 0.250420i | \(-0.0805685\pi\) | |||||||
\(488\) | − | 5006.59i | − | 0.464422i | ||||||
\(489\) | −10385.6 | −0.960437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3456.93 | −0.317737 | −0.158869 | − | 0.987300i | \(-0.550785\pi\) | ||||
−0.158869 | + | 0.987300i | \(0.550785\pi\) | |||||||
\(492\) | 9407.67i | 0.862054i | ||||||||
\(493\) | − | 1409.64i | − | 0.128777i | ||||||
\(494\) | 5807.06 | 0.528891 | ||||||||
\(495\) | 4384.30 | − | 6506.47i | 0.398100 | − | 0.590796i | ||||
\(496\) | 2577.86 | 0.233365 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 1512.35i | − | 0.136084i | ||||||
\(499\) | 12098.2 | 1.08535 | 0.542674 | − | 0.839943i | \(-0.317412\pi\) | ||||
0.542674 | + | 0.839943i | \(0.317412\pi\) | |||||||
\(500\) | −5469.62 | − | 1154.68i | −0.489217 | − | 0.103278i | ||||
\(501\) | −10247.7 | −0.913842 | ||||||||
\(502\) | − | 1525.09i | − | 0.135593i | ||||||
\(503\) | 1508.10i | 0.133684i | 0.997764 | + | 0.0668418i | \(0.0212923\pi\) | ||||
−0.997764 | + | 0.0668418i | \(0.978708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11047.2 | + | 16394.5i | −0.973454 | + | 1.44464i | ||||
\(506\) | 2036.87 | 0.178952 | ||||||||
\(507\) | − | 42151.1i | − | 3.69230i | ||||||
\(508\) | − | 3885.74i | − | 0.339374i | ||||||
\(509\) | 10363.5 | 0.902460 | 0.451230 | − | 0.892408i | \(-0.350985\pi\) | ||||
0.451230 | + | 0.892408i | \(0.350985\pi\) | |||||||
\(510\) | −2422.64 | − | 1632.46i | −0.210346 | − | 0.141739i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 2500.37i | 0.215193i | ||||||||
\(514\) | −4604.72 | −0.395147 | ||||||||
\(515\) | 7875.54 | + | 5306.82i | 0.673860 | + | 0.454071i | ||||
\(516\) | −6558.76 | −0.559561 | ||||||||
\(517\) | − | 22682.8i | − | 1.92957i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11225.2 | −0.949383 | ||||||||
\(520\) | 4672.62 | − | 6934.36i | 0.394054 | − | 0.584792i | ||||
\(521\) | 4650.70 | 0.391077 | 0.195538 | − | 0.980696i | \(-0.437355\pi\) | ||||
0.195538 | + | 0.980696i | \(0.437355\pi\) | |||||||
\(522\) | − | 2016.33i | − | 0.169066i | ||||||
\(523\) | 6457.71i | 0.539916i | 0.962872 | + | 0.269958i | \(0.0870098\pi\) | ||||
−0.962872 | + | 0.269958i | \(0.912990\pi\) | |||||||
\(524\) | −598.374 | −0.0498856 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9667.00 | −0.801333 | ||||||||
\(527\) | 3267.32i | 0.270069i | ||||||||
\(528\) | 4987.35i | 0.411073i | ||||||||
\(529\) | 11724.0 | 0.963586 | ||||||||
\(530\) | −7336.65 | + | 10887.9i | −0.601290 | + | 0.892339i | ||||
\(531\) | 7787.59 | 0.636446 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 34129.6i | − | 2.77358i | ||||||
\(534\) | 789.299 | 0.0639631 | ||||||||
\(535\) | −11891.8 | − | 8013.13i | −0.960986 | − | 0.647548i | ||||
\(536\) | 984.590 | 0.0793429 | ||||||||
\(537\) | 15650.8i | 1.25769i | ||||||||
\(538\) | 9660.70i | 0.774168i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2985.76 | + | 2011.91i | 0.237938 | + | 0.160331i | ||||
\(541\) | −23030.2 | −1.83021 | −0.915106 | − | 0.403214i | \(-0.867893\pi\) | ||||
−0.915106 | + | 0.403214i | \(0.867893\pi\) | |||||||
\(542\) | 11900.7i | 0.943137i | ||||||||
\(543\) | 16934.4i | 1.33835i | ||||||||
\(544\) | 648.936 | 0.0511451 | ||||||||
\(545\) | −3738.60 | + | 5548.24i | −0.293842 | + | 0.436074i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6553.72i | 0.512280i | 0.966640 | + | 0.256140i | \(0.0824508\pi\) | ||||
−0.966640 | + | 0.256140i | \(0.917549\pi\) | |||||||
\(548\) | 1980.98i | 0.154422i | ||||||||
\(549\) | 9076.66 | 0.705614 | ||||||||
\(550\) | −11211.2 | + | 4541.66i | −0.869174 | + | 0.352104i | ||||
\(551\) | −2158.90 | −0.166919 | ||||||||
\(552\) | − | 1084.82i | − | 0.0836469i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15337.8 | 1.17625 | ||||||||
\(555\) | 6543.85 | − | 9711.33i | 0.500488 | − | 0.742745i | ||||
\(556\) | −1866.08 | −0.142337 | ||||||||
\(557\) | − | 5254.73i | − | 0.399731i | −0.979823 | − | 0.199865i | \(-0.935949\pi\) | ||
0.979823 | − | 0.199865i | \(-0.0640505\pi\) | |||||||
\(558\) | 4673.51i | 0.354561i | ||||||||
\(559\) | 23794.2 | 1.80034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6321.24 | −0.475727 | ||||||||
\(562\) | 12628.4i | 0.947856i | ||||||||
\(563\) | 9759.11i | 0.730546i | 0.930900 | + | 0.365273i | \(0.119024\pi\) | ||||
−0.930900 | + | 0.365273i | \(0.880976\pi\) | |||||||
\(564\) | −12080.7 | −0.901931 | ||||||||
\(565\) | 7975.78 | + | 5374.37i | 0.593882 | + | 0.400179i | ||||
\(566\) | 12245.4 | 0.909389 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1680.48i | 0.124140i | ||||||||
\(569\) | −4063.44 | −0.299382 | −0.149691 | − | 0.988733i | \(-0.547828\pi\) | ||||
−0.149691 | + | 0.988733i | \(0.547828\pi\) | |||||||
\(570\) | −2500.15 | + | 3710.32i | −0.183719 | + | 0.272646i | ||||
\(571\) | −23907.0 | −1.75215 | −0.876075 | − | 0.482175i | \(-0.839847\pi\) | ||||
−0.876075 | + | 0.482175i | \(0.839847\pi\) | |||||||
\(572\) | − | 18093.4i | − | 1.32259i | ||||||
\(573\) | 7246.48i | 0.528317i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2438.60 | − | 987.879i | 0.176863 | − | 0.0716477i | ||||
\(576\) | 928.226 | 0.0671460 | ||||||||
\(577\) | 15145.4i | 1.09274i | 0.837545 | + | 0.546369i | \(0.183990\pi\) | ||||
−0.837545 | + | 0.546369i | \(0.816010\pi\) | |||||||
\(578\) | − | 9003.50i | − | 0.647918i | ||||||
\(579\) | 14276.7 | 1.02473 | ||||||||
\(580\) | −1737.15 | + | 2577.99i | −0.124364 | + | 0.184561i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5626.13i | 0.400706i | ||||||||
\(583\) | 28409.0i | 2.01815i | ||||||||
\(584\) | 1134.27 | 0.0803704 | ||||||||
\(585\) | 12571.6 | + | 8471.19i | 0.888498 | + | 0.598702i | ||||
\(586\) | −3293.34 | −0.232162 | ||||||||
\(587\) | 10865.9i | 0.764025i | 0.924157 | + | 0.382013i | \(0.124769\pi\) | ||||
−0.924157 | + | 0.382013i | \(0.875231\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5003.96 | 0.350059 | ||||||||
\(590\) | −9956.90 | − | 6709.32i | −0.694778 | − | 0.468167i | ||||
\(591\) | 20135.8 | 1.40149 | ||||||||
\(592\) | 2601.31i | 0.180596i | ||||||||
\(593\) | − | 4578.29i | − | 0.317045i | −0.987355 | − | 0.158523i | \(-0.949327\pi\) | ||
0.987355 | − | 0.158523i | \(-0.0506731\pi\) | |||||||
\(594\) | 7790.53 | 0.538130 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −714.214 | −0.0490862 | ||||||||
\(597\) | − | 29243.9i | − | 2.00481i | ||||||
\(598\) | 3935.57i | 0.269126i | ||||||||
\(599\) | 20561.5 | 1.40254 | 0.701270 | − | 0.712896i | \(-0.252617\pi\) | ||||
0.701270 | + | 0.712896i | \(0.252617\pi\) | |||||||
\(600\) | 2418.86 | + | 5970.98i | 0.164582 | + | 0.406274i | ||||
\(601\) | −1254.44 | −0.0851406 | −0.0425703 | − | 0.999093i | \(-0.513555\pi\) | ||||
−0.0425703 | + | 0.999093i | \(0.513555\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1785.00i | 0.120549i | ||||||||
\(604\) | −3326.67 | −0.224107 | ||||||||
\(605\) | −6310.60 | + | 9365.18i | −0.424070 | + | 0.629337i | ||||
\(606\) | 22782.7 | 1.52720 | ||||||||
\(607\) | − | 10861.4i | − | 0.726277i | −0.931735 | − | 0.363139i | \(-0.881705\pi\) | ||
0.931735 | − | 0.363139i | \(-0.118295\pi\) | |||||||
\(608\) | − | 993.859i | − | 0.0662933i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11605.0 | − | 7819.90i | −0.770286 | − | 0.519047i | ||||
\(611\) | 43826.9 | 2.90188 | ||||||||
\(612\) | 1176.48i | 0.0777067i | ||||||||
\(613\) | − | 21385.7i | − | 1.40907i | −0.709668 | − | 0.704536i | \(-0.751155\pi\) | ||
0.709668 | − | 0.704536i | \(-0.248845\pi\) | |||||||
\(614\) | 15780.8 | 1.03724 | ||||||||
\(615\) | 21806.5 | + | 14694.0i | 1.42980 | + | 0.963448i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11863.3i | − | 0.774066i | −0.922066 | − | 0.387033i | \(-0.873500\pi\) | ||
0.922066 | − | 0.387033i | \(-0.126500\pi\) | |||||||
\(618\) | − | 10944.3i | − | 0.712370i | ||||||
\(619\) | 8098.60 | 0.525864 | 0.262932 | − | 0.964814i | \(-0.415310\pi\) | ||||
0.262932 | + | 0.964814i | \(0.415310\pi\) | |||||||
\(620\) | 4026.41 | − | 5975.35i | 0.260814 | − | 0.387058i | ||||
\(621\) | −1694.56 | −0.109501 | ||||||||
\(622\) | 6873.96i | 0.443120i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9636.39 | −0.618212 | ||||||||
\(625\) | −11219.6 | + | 10874.8i | −0.718055 | + | 0.695987i | ||||
\(626\) | 14419.6 | 0.920645 | ||||||||
\(627\) | 9681.10i | 0.616628i | ||||||||
\(628\) | 670.787i | 0.0426231i | ||||||||
\(629\) | −3297.04 | −0.209001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28405.4 | 1.79208 | 0.896038 | − | 0.443977i | \(-0.146433\pi\) | ||||
0.896038 | + | 0.443977i | \(0.146433\pi\) | |||||||
\(632\) | − | 4107.39i | − | 0.258518i | ||||||
\(633\) | 16237.3i | 1.01955i | ||||||||
\(634\) | 1771.61 | 0.110977 | ||||||||
\(635\) | −9006.96 | − | 6069.22i | −0.562883 | − | 0.379291i | ||||
\(636\) | 15130.4 | 0.943335 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6726.58i | 0.417411i | ||||||||
\(639\) | −3046.62 | −0.188611 | ||||||||
\(640\) | −1186.79 | − | 799.703i | −0.0733001 | − | 0.0493923i | ||||
\(641\) | 4854.85 | 0.299150 | 0.149575 | − | 0.988750i | \(-0.452209\pi\) | ||||
0.149575 | + | 0.988750i | \(0.452209\pi\) | |||||||
\(642\) | 16525.5i | 1.01591i | ||||||||
\(643\) | − | 23838.8i | − | 1.46207i | −0.682342 | − | 0.731033i | \(-0.739038\pi\) | ||
0.682342 | − | 0.731033i | \(-0.260962\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10244.3 | + | 15202.9i | −0.625376 | + | 0.928083i | ||||
\(646\) | 1259.67 | 0.0767199 | ||||||||
\(647\) | 16912.8i | 1.02768i | 0.857886 | + | 0.513841i | \(0.171778\pi\) | ||||
−0.857886 | + | 0.513841i | \(0.828222\pi\) | |||||||
\(648\) | − | 7281.94i | − | 0.441453i | ||||||
\(649\) | −25979.9 | −1.57134 | ||||||||
\(650\) | −8775.25 | − | 21661.8i | −0.529529 | − | 1.30715i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6448.37i | − | 0.387327i | ||||||
\(653\) | − | 14301.5i | − | 0.857059i | −0.903528 | − | 0.428530i | \(-0.859032\pi\) | ||
0.903528 | − | 0.428530i | \(-0.140968\pi\) | |||||||
\(654\) | 7710.15 | 0.460995 | ||||||||
\(655\) | −934.612 | + | 1387.00i | −0.0557532 | + | 0.0827399i | ||||
\(656\) | −5841.17 | −0.347651 | ||||||||
\(657\) | 2056.36i | 0.122110i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8601.03 | 0.508420 | 0.254210 | − | 0.967149i | \(-0.418185\pi\) | ||||
0.254210 | + | 0.967149i | \(0.418185\pi\) | |||||||
\(660\) | 11560.4 | + | 7789.84i | 0.681802 | + | 0.459423i | ||||
\(661\) | −794.288 | −0.0467386 | −0.0233693 | − | 0.999727i | \(-0.507439\pi\) | ||||
−0.0233693 | + | 0.999727i | \(0.507439\pi\) | |||||||
\(662\) | 3532.37i | 0.207386i | ||||||||
\(663\) | − | 12213.7i | − | 0.715445i | ||||||
\(664\) | 939.007 | 0.0548803 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4716.02 | −0.274387 | ||||||||
\(667\) | − | 1463.13i | − | 0.0849366i | ||||||
\(668\) | − | 6362.75i | − | 0.368536i | ||||||
\(669\) | −37369.2 | −2.15961 | ||||||||
\(670\) | 1537.85 | − | 2282.23i | 0.0886752 | − | 0.131597i | ||||
\(671\) | −30280.3 | −1.74211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3100.85i | − | 0.177606i | −0.996049 | − | 0.0888031i | \(-0.971696\pi\) | ||
0.996049 | − | 0.0888031i | \(-0.0283042\pi\) | |||||||
\(674\) | 15042.7 | 0.859677 | ||||||||
\(675\) | 9327.03 | − | 3778.40i | 0.531848 | − | 0.215453i | ||||
\(676\) | 26171.4 | 1.48904 | ||||||||
\(677\) | 3236.73i | 0.183748i | 0.995771 | + | 0.0918742i | \(0.0292858\pi\) | ||||
−0.995771 | + | 0.0918742i | \(0.970714\pi\) | |||||||
\(678\) | − | 11083.6i | − | 0.627822i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1013.59 | − | 1504.20i | 0.0571607 | − | 0.0848288i | ||||
\(681\) | 42689.8 | 2.40217 | ||||||||
\(682\) | − | 15591.1i | − | 0.875386i | ||||||
\(683\) | − | 9415.00i | − | 0.527460i | −0.964597 | − | 0.263730i | \(-0.915047\pi\) | ||
0.964597 | − | 0.263730i | \(-0.0849527\pi\) | |||||||
\(684\) | 1801.81 | 0.100722 | ||||||||
\(685\) | 4591.82 | + | 3094.14i | 0.256123 | + | 0.172585i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3271.70i | − | 0.181693i | ||||||
\(688\) | − | 4072.29i | − | 0.225661i | ||||||
\(689\) | −54891.0 | −3.03509 | ||||||||
\(690\) | −2514.57 | − | 1694.41i | −0.138736 | − | 0.0934855i | ||||
\(691\) | −22798.5 | −1.25513 | −0.627565 | − | 0.778564i | \(-0.715948\pi\) | ||||
−0.627565 | + | 0.778564i | \(0.715948\pi\) | |||||||
\(692\) | − | 6969.63i | − | 0.382870i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9317.06 | 0.509612 | ||||||||
\(695\) | −2914.67 | + | 4325.49i | −0.159079 | + | 0.236079i | ||||
\(696\) | 3582.53 | 0.195108 | ||||||||
\(697\) | − | 7403.41i | − | 0.402330i | ||||||
\(698\) | − | 14396.3i | − | 0.780670i | ||||||
\(699\) | 40637.0 | 2.19890 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33797.9 | 1.82101 | 0.910506 | − | 0.413496i | \(-0.135692\pi\) | ||||
0.910506 | + | 0.413496i | \(0.135692\pi\) | |||||||
\(702\) | 15052.6i | 0.809294i | ||||||||
\(703\) | 5049.48i | 0.270903i | ||||||||
\(704\) | −3096.62 | −0.165779 | ||||||||
\(705\) | −18869.1 | + | 28002.5i | −1.00802 | + | 1.49593i | ||||
\(706\) | 7280.16 | 0.388091 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13836.7i | 0.734484i | ||||||||
\(709\) | 26226.1 | 1.38920 | 0.694599 | − | 0.719397i | \(-0.255582\pi\) | ||||
0.694599 | + | 0.719397i | \(0.255582\pi\) | |||||||
\(710\) | 3895.28 | + | 2624.78i | 0.205898 | + | 0.138741i | ||||
\(711\) | 7446.45 | 0.392776 | ||||||||
\(712\) | 490.071i | 0.0257952i | ||||||||
\(713\) | 3391.29i | 0.178128i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −41939.5 | − | 28260.4i | −2.19364 | − | 1.47815i | ||||
\(716\) | −9717.47 | −0.507205 | ||||||||
\(717\) | 29732.1i | 1.54863i | ||||||||
\(718\) | − | 10939.8i | − | 0.568620i | ||||||
\(719\) | 8593.89 | 0.445755 | 0.222878 | − | 0.974846i | \(-0.428455\pi\) | ||||
0.222878 | + | 0.974846i | \(0.428455\pi\) | |||||||
\(720\) | 1449.82 | − | 2151.58i | 0.0750436 | − | 0.111368i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 11788.8i | 0.607664i | ||||||||
\(723\) | 9990.14i | 0.513883i | ||||||||
\(724\) | −10514.4 | −0.539732 | ||||||||
\(725\) | 3262.38 | + | 8053.24i | 0.167120 | + | 0.412538i | ||||
\(726\) | 13014.4 | 0.665303 | ||||||||
\(727\) | − | 26368.9i | − | 1.34521i | −0.740001 | − | 0.672606i | \(-0.765175\pi\) | ||
0.740001 | − | 0.672606i | \(-0.234825\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −801.754 | −0.0407333 | ||||||||
\(730\) | 1771.64 | − | 2629.18i | 0.0898235 | − | 0.133302i | ||||
\(731\) | 5161.45 | 0.261153 | ||||||||
\(732\) | 16127.0i | 0.814307i | ||||||||
\(733\) | 16495.5i | 0.831207i | 0.909546 | + | 0.415604i | \(0.136430\pi\) | ||||
−0.909546 | + | 0.415604i | \(0.863570\pi\) | |||||||
\(734\) | −130.174 | −0.00654607 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 673.560 | 0.0337333 | ||||||||
\(737\) | − | 5954.87i | − | 0.297626i | ||||||
\(738\) | − | 10589.7i | − | 0.528200i | ||||||
\(739\) | −8670.04 | −0.431573 | −0.215786 | − | 0.976441i | \(-0.569232\pi\) | ||||
−0.215786 | + | 0.976441i | \(0.569232\pi\) | |||||||
\(740\) | 6029.71 | + | 4063.04i | 0.299536 | + | 0.201838i | ||||
\(741\) | −18705.5 | −0.927346 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30923.0i | 1.52686i | 0.645891 | + | 0.763430i | \(0.276486\pi\) | ||||
−0.645891 | + | 0.763430i | \(0.723514\pi\) | |||||||
\(744\) | −8303.70 | −0.409178 | ||||||||
\(745\) | −1115.55 | + | 1655.51i | −0.0548596 | + | 0.0814139i | ||||
\(746\) | 20306.8 | 0.996627 | ||||||||
\(747\) | 1702.36i | 0.0833819i | ||||||||
\(748\) | − | 3924.82i | − | 0.191852i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17618.5 | + | 3719.41i | 0.857783 | + | 0.181085i | ||||
\(751\) | 13168.0 | 0.639822 | 0.319911 | − | 0.947448i | \(-0.396347\pi\) | ||||
0.319911 | + | 0.947448i | \(0.396347\pi\) | |||||||
\(752\) | − | 7500.83i | − | 0.363733i | ||||||
\(753\) | 4912.55i | 0.237747i | ||||||||
\(754\) | −12996.9 | −0.627743 | ||||||||
\(755\) | −5196.00 | + | 7711.07i | −0.250466 | + | 0.371701i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31713.3i | 1.52264i | 0.648375 | + | 0.761321i | \(0.275449\pi\) | ||||
−0.648375 | + | 0.761321i | \(0.724551\pi\) | |||||||
\(758\) | 2907.91i | 0.139341i | ||||||||
\(759\) | −6561.09 | −0.313771 | ||||||||
\(760\) | −2303.72 | − | 1552.33i | −0.109953 | − | 0.0740906i | ||||
\(761\) | −818.651 | −0.0389962 | −0.0194981 | − | 0.999810i | \(-0.506207\pi\) | ||||
−0.0194981 | + | 0.999810i | \(0.506207\pi\) | |||||||
\(762\) | 12516.6i | 0.595051i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4499.29 | −0.213061 | ||||||||
\(765\) | 2727.03 | + | 1837.57i | 0.128884 | + | 0.0868466i | ||||
\(766\) | −1154.60 | −0.0544615 | ||||||||
\(767\) | − | 50197.4i | − | 2.36313i | ||||||
\(768\) | 1649.23i | 0.0774891i | ||||||||
\(769\) | −28514.9 | −1.33716 | −0.668578 | − | 0.743642i | \(-0.733097\pi\) | ||||
−0.668578 | + | 0.743642i | \(0.733097\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14832.6 | 0.692842 | ||||||||
\(772\) | 8864.33i | 0.413257i | ||||||||
\(773\) | − | 28791.0i | − | 1.33964i | −0.742525 | − | 0.669819i | \(-0.766372\pi\) | ||
0.742525 | − | 0.669819i | \(-0.233628\pi\) | |||||||
\(774\) | 7382.83 | 0.342856 | ||||||||
\(775\) | −7561.65 | − | 18666.1i | −0.350481 | − | 0.865167i | ||||
\(776\) | −3493.23 | −0.161598 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 4142.00i | − | 0.190871i | ||||||
\(779\) | −11338.5 | −0.521493 | ||||||||
\(780\) | −15051.3 | + | 22336.7i | −0.690926 | + | 1.02536i | ||||
\(781\) | 10163.7 | 0.465666 | ||||||||
\(782\) | 853.706i | 0.0390390i | ||||||||
\(783\) | − | 5596.12i | − | 0.255414i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1554.85 | + | 1047.72i | 0.0706943 | + | 0.0476364i | ||||
\(786\) | 1927.46 | 0.0874684 | ||||||||
\(787\) | 7485.80i | 0.339059i | 0.985525 | + | 0.169530i | \(0.0542249\pi\) | ||||
−0.985525 | + | 0.169530i | \(0.945775\pi\) | |||||||
\(788\) | 12502.2i | 0.565194i | ||||||||
\(789\) | 31139.0 | 1.40504 | ||||||||
\(790\) | −9520.73 | − | 6415.42i | −0.428775 | − | 0.288924i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 5613.98i | − | 0.251874i | ||||||
\(793\) | − | 58506.5i | − | 2.61996i | ||||||
\(794\) | −10066.8 | −0.449948 | ||||||||
\(795\) | 23632.5 | − | 35071.6i | 1.05429 | − | 1.56461i | ||||
\(796\) | 18157.4 | 0.808506 | ||||||||
\(797\) | 2323.41i | 0.103261i | 0.998666 | + | 0.0516307i | \(0.0164419\pi\) | ||||
−0.998666 | + | 0.0516307i | \(0.983558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9506.96 | 0.420941 | ||||||||
\(800\) | −3707.35 | + | 1501.85i | −0.163843 | + | 0.0663732i | ||||
\(801\) | −888.469 | −0.0391917 | ||||||||
\(802\) | 9893.76i | 0.435612i | ||||||||
\(803\) | − | 6860.14i | − | 0.301481i | ||||||
\(804\) | −3171.52 | −0.139118 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30124.6 | 1.31649 | ||||||||
\(807\) | − | 31118.7i | − | 1.35741i | ||||||
\(808\) | 14145.7i | 0.615895i | ||||||||
\(809\) | 9103.69 | 0.395635 | 0.197818 | − | 0.980239i | \(-0.436615\pi\) | ||||
0.197818 | + | 0.980239i | \(0.436615\pi\) | |||||||
\(810\) | −16879.2 | − | 11373.8i | −0.732191 | − | 0.493377i | ||||
\(811\) | −4516.19 | −0.195542 | −0.0977711 | − | 0.995209i | \(-0.531171\pi\) | ||||
−0.0977711 | + | 0.995209i | \(0.531171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 38334.2i | − | 1.65368i | ||||||
\(814\) | 15732.9 | 0.677443 | ||||||||
\(815\) | −14947.0 | − | 10071.8i | −0.642418 | − | 0.432885i | ||||
\(816\) | −2090.33 | −0.0896767 | ||||||||
\(817\) | − | 7904.86i | − | 0.338502i | ||||||
\(818\) | − | 18779.7i | − | 0.802709i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9123.44 | + | 13539.5i | −0.388542 | + | 0.576612i | ||||
\(821\) | −6046.44 | −0.257031 | −0.128515 | − | 0.991708i | \(-0.541021\pi\) | ||||
−0.128515 | + | 0.991708i | \(0.541021\pi\) | |||||||
\(822\) | − | 6381.06i | − | 0.270760i | ||||||
\(823\) | 44591.3i | 1.88864i | 0.329022 | + | 0.944322i | \(0.393281\pi\) | ||||
−0.329022 | + | 0.944322i | \(0.606719\pi\) | |||||||
\(824\) | 6795.25 | 0.287286 | ||||||||
\(825\) | 36113.0 | − | 14629.4i | 1.52399 | − | 0.617371i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17170.6i | − | 0.721982i | −0.932569 | − | 0.360991i | \(-0.882439\pi\) | ||
0.932569 | − | 0.360991i | \(-0.117561\pi\) | |||||||
\(828\) | 1221.12i | 0.0512524i | ||||||||
\(829\) | 30509.9 | 1.27823 | 0.639115 | − | 0.769111i | \(-0.279301\pi\) | ||||
0.639115 | + | 0.769111i | \(0.279301\pi\) | |||||||
\(830\) | 1466.65 | − | 2176.57i | 0.0613353 | − | 0.0910241i | ||||
\(831\) | −49405.5 | −2.06241 | ||||||||
\(832\) | − | 5983.18i | − | 0.249314i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6010.95 | 0.249571 | ||||||||
\(835\) | −14748.6 | − | 9938.12i | −0.611251 | − | 0.411883i | ||||
\(836\) | −6010.93 | −0.248675 | ||||||||
\(837\) | 12970.9i | 0.535650i | ||||||||
\(838\) | 16847.5i | 0.694497i | ||||||||
\(839\) | 34089.6 | 1.40275 | 0.701373 | − | 0.712794i | \(-0.252571\pi\) | ||||
0.701373 | + | 0.712794i | \(0.252571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19557.1 | −0.801884 | ||||||||
\(842\) | − | 11360.3i | − | 0.464966i | ||||||
\(843\) | − | 40678.0i | − | 1.66195i | ||||||
\(844\) | −10081.6 | −0.411165 | ||||||||
\(845\) | 40877.6 | − | 60664.0i | 1.66418 | − | 2.46971i | ||||
\(846\) | 13598.6 | 0.552634 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9394.40i | 0.380430i | ||||||||
\(849\) | −39444.6 | −1.59450 | ||||||||
\(850\) | −1903.53 | − | 4698.89i | −0.0768124 | − | 0.189613i | ||||
\(851\) | −3422.14 | −0.137849 | ||||||||
\(852\) | − | 5413.11i | − | 0.217664i | ||||||
\(853\) | − | 5078.39i | − | 0.203846i | −0.994792 | − | 0.101923i | \(-0.967500\pi\) | ||
0.994792 | − | 0.101923i | \(-0.0324995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2814.28 | − | 4176.50i | 0.112569 | − | 0.167057i | ||||
\(856\) | −10260.6 | −0.409697 | ||||||||
\(857\) | 85.5262i | 0.00340901i | 0.999999 | + | 0.00170450i | \(0.000542561\pi\) | ||||
−0.999999 | + | 0.00170450i | \(0.999457\pi\) | |||||||
\(858\) | 58281.6i | 2.31900i | ||||||||
\(859\) | −32320.1 | −1.28376 | −0.641878 | − | 0.766807i | \(-0.721844\pi\) | ||||
−0.641878 | + | 0.766807i | \(0.721844\pi\) | |||||||
\(860\) | −9439.39 | − | 6360.60i | −0.374279 | − | 0.252203i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 24696.7i | − | 0.975840i | ||||||
\(863\) | 20936.2i | 0.825813i | 0.910773 | + | 0.412907i | \(0.135486\pi\) | ||||
−0.910773 | + | 0.412907i | \(0.864514\pi\) | |||||||
\(864\) | 2576.20 | 0.101440 | ||||||||
\(865\) | −16155.3 | − | 10886.0i | −0.635024 | − | 0.427902i | ||||
\(866\) | 18063.9 | 0.708816 | ||||||||
\(867\) | 29001.7i | 1.13604i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24841.8 | −0.969736 | ||||||||
\(870\) | 5595.63 | − | 8304.13i | 0.218057 | − | 0.323605i | ||||
\(871\) | 11505.8 | 0.447600 | ||||||||
\(872\) | 4787.19i | 0.185911i | ||||||||
\(873\) | − | 6333.02i | − | 0.245522i | ||||||
\(874\) | 1307.47 | 0.0506015 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3653.66 | −0.140920 | ||||||||
\(877\) | 24078.1i | 0.927093i | 0.886073 | + | 0.463546i | \(0.153423\pi\) | ||||
−0.886073 | + | 0.463546i | \(0.846577\pi\) | |||||||
\(878\) | − | 21314.8i | − | 0.819295i | ||||||
\(879\) | 10608.4 | 0.407067 | ||||||||
\(880\) | −4836.67 | + | 7177.81i | −0.185277 | + | 0.274959i | ||||
\(881\) | 23196.8 | 0.887081 | 0.443541 | − | 0.896254i | \(-0.353722\pi\) | ||||
0.443541 | + | 0.896254i | \(0.353722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31800.2i | 1.21196i | 0.795479 | + | 0.605981i | \(0.207219\pi\) | ||||
−0.795479 | + | 0.605981i | \(0.792781\pi\) | |||||||
\(884\) | 7583.40 | 0.288526 | ||||||||
\(885\) | 32072.8 | + | 21611.8i | 1.21821 | + | 0.820873i | ||||
\(886\) | −1802.64 | −0.0683532 | ||||||||
\(887\) | 34200.2i | 1.29462i | 0.762226 | + | 0.647311i | \(0.224107\pi\) | ||||
−0.762226 | + | 0.647311i | \(0.775893\pi\) | |||||||
\(888\) | − | 8379.24i | − | 0.316654i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1135.96 | + | 765.452i | 0.0427837 | + | 0.0288292i | ||||
\(891\) | −44041.8 | −1.65595 | ||||||||
\(892\) | − | 23202.3i | − | 0.870931i | ||||||
\(893\) | − | 14560.1i | − | 0.545616i | ||||||
\(894\) | 2300.60 | 0.0860666 | ||||||||
\(895\) | −15177.9 | + | 22524.6i | −0.566862 | + | 0.841246i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12677.1i | − | 0.471880i | ||||||
\(898\) | − | 15543.8i | − | 0.577619i | ||||||
\(899\) | −11199.4 | −0.415486 | ||||||||
\(900\) | −2722.77 | − | 6721.20i | −0.100843 | − | 0.248934i | ||||
\(901\) | −11907.0 | −0.440265 | ||||||||
\(902\) | 35327.8i | 1.30409i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6881.74 | 0.253190 | ||||||||
\(905\) | −16422.7 | + | 24372.0i | −0.603215 | + | 0.895195i | ||||
\(906\) | 10715.7 | 0.392944 | ||||||||
\(907\) | 4793.39i | 0.175482i | 0.996143 | + | 0.0877409i | \(0.0279648\pi\) | ||||
−0.996143 | + | 0.0877409i | \(0.972035\pi\) | |||||||
\(908\) | 26505.9i | 0.968753i | ||||||||
\(909\) | −25645.3 | −0.935753 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25153.4 | −0.914787 | −0.457393 | − | 0.889264i | \(-0.651217\pi\) | ||||
−0.457393 | + | 0.889264i | \(0.651217\pi\) | |||||||
\(912\) | 3201.38i | 0.116237i | ||||||||
\(913\) | − | 5679.19i | − | 0.205864i | ||||||
\(914\) | −5520.70 | −0.199791 | ||||||||
\(915\) | 37381.7 | + | 25189.2i | 1.35060 | + | 0.910085i | ||||
\(916\) | 2031.38 | 0.0732736 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3265.22i | 0.117395i | ||||||||
\(919\) | 20437.0 | 0.733573 | 0.366786 | − | 0.930305i | \(-0.380458\pi\) | ||||
0.366786 | + | 0.930305i | \(0.380458\pi\) | |||||||
\(920\) | 1052.05 | − | 1561.28i | 0.0377010 | − | 0.0559499i | ||||
\(921\) | −50832.6 | −1.81867 | ||||||||
\(922\) | 32964.7i | 1.17748i | ||||||||
\(923\) | 19637.9i | 0.700315i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18835.9 | − | 7630.44i | 0.669534 | − | 0.271229i | ||||
\(926\) | 19898.3 | 0.706155 | ||||||||
\(927\) | 12319.4i | 0.436485i | ||||||||
\(928\) | 2224.37i | 0.0786838i | ||||||||
\(929\) | −1282.13 | −0.0452802 | −0.0226401 | − | 0.999744i | \(-0.507207\pi\) | ||||
−0.0226401 | + | 0.999744i | \(0.507207\pi\) | |||||||
\(930\) | −12969.7 | + | 19247.6i | −0.457305 | + | 0.678659i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25231.3i | 0.886779i | ||||||||
\(933\) | − | 22142.1i | − | 0.776957i | ||||||
\(934\) | −4203.11 | −0.147248 | ||||||||
\(935\) | −9097.54 | − | 6130.25i | −0.318205 | − | 0.214418i | ||||
\(936\) | 10847.1 | 0.378793 | ||||||||
\(937\) | − | 16878.5i | − | 0.588472i | −0.955733 | − | 0.294236i | \(-0.904935\pi\) | ||
0.955733 | − | 0.294236i | \(-0.0950651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46447.9 | −1.61424 | ||||||||
\(940\) | −17386.6 | − | 11715.7i | −0.603284 | − | 0.406515i | ||||
\(941\) | 14931.6 | 0.517275 | 0.258637 | − | 0.965974i | \(-0.416726\pi\) | ||||
0.258637 | + | 0.965974i | \(0.416726\pi\) | |||||||
\(942\) | − | 2160.71i | − | 0.0747344i | ||||||
\(943\) | − | 7684.33i | − | 0.265362i | ||||||
\(944\) | −8591.11 | −0.296204 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24629.5 | −0.846486 | ||||||||
\(947\) | 37545.7i | 1.28835i | 0.764877 | + | 0.644177i | \(0.222800\pi\) | ||||
−0.764877 | + | 0.644177i | \(0.777200\pi\) | |||||||
\(948\) | 13230.6i | 0.453279i | ||||||||
\(949\) | 13254.9 | 0.453396 | ||||||||
\(950\) | −7196.45 | + | 2915.29i | −0.245772 | + | 0.0995628i | ||||
\(951\) | −5706.63 | −0.194585 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 437.260i | − | 0.0148628i | −0.999972 | − | 0.00743140i | \(-0.997634\pi\) | ||
0.999972 | − | 0.00743140i | \(-0.00236551\pi\) | |||||||
\(954\) | −17031.5 | −0.578003 | ||||||||
\(955\) | −7027.54 | + | 10429.1i | −0.238121 | + | 0.353381i | ||||
\(956\) | −18460.5 | −0.624535 | ||||||||
\(957\) | − | 21667.4i | − | 0.731879i | ||||||
\(958\) | − | 16019.9i | − | 0.540272i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3822.85 | + | 2575.97i | 0.128523 | + | 0.0866033i | ||||
\(961\) | −3832.58 | −0.128649 | ||||||||
\(962\) | 30398.6i | 1.01881i | ||||||||
\(963\) | − | 18601.9i | − | 0.622469i | ||||||
\(964\) | −6202.82 | −0.207240 | ||||||||
\(965\) | 20547.1 | + | 13845.4i | 0.685424 | + | 0.461864i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52372.7i | − | 1.74167i | −0.491577 | − | 0.870834i | \(-0.663579\pi\) | ||
0.491577 | − | 0.870834i | \(-0.336421\pi\) | |||||||
\(968\) | 8080.57i | 0.268305i | ||||||||
\(969\) | −4057.60 | −0.134519 | ||||||||
\(970\) | −5456.15 | + | 8097.14i | −0.180605 | + | 0.268024i | ||||
\(971\) | 40759.4 | 1.34710 | 0.673548 | − | 0.739144i | \(-0.264769\pi\) | ||||
0.673548 | + | 0.739144i | \(0.264769\pi\) | |||||||
\(972\) | 14761.6i | 0.487119i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10765.2 | −0.354147 | ||||||||
\(975\) | 28266.5 | + | 69776.3i | 0.928464 | + | 2.29193i | ||||
\(976\) | −10013.2 | −0.328396 | ||||||||
\(977\) | − | 37637.9i | − | 1.23249i | −0.787554 | − | 0.616246i | \(-0.788653\pi\) | ||
0.787554 | − | 0.616246i | \(-0.211347\pi\) | |||||||
\(978\) | 20771.2i | 0.679132i | ||||||||
\(979\) | 2963.99 | 0.0967614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8678.89 | −0.282462 | ||||||||
\(982\) | 6913.86i | 0.224674i | ||||||||
\(983\) | − | 8799.74i | − | 0.285522i | −0.989757 | − | 0.142761i | \(-0.954402\pi\) | ||
0.989757 | − | 0.142761i | \(-0.0455980\pi\) | |||||||
\(984\) | 18815.3 | 0.609564 | ||||||||
\(985\) | 28979.6 | + | 19527.5i | 0.937427 | + | 0.631672i | ||||
\(986\) | −2819.29 | −0.0910592 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 11614.1i | − | 0.373982i | ||||||
\(989\) | 5357.29 | 0.172247 | ||||||||
\(990\) | −13012.9 | − | 8768.59i | −0.417756 | − | 0.281499i | ||||
\(991\) | −43972.1 | −1.40950 | −0.704752 | − | 0.709454i | \(-0.748942\pi\) | ||||
−0.704752 | + | 0.709454i | \(0.748942\pi\) | |||||||
\(992\) | − | 5155.72i | − | 0.165014i | ||||||
\(993\) | − | 11378.3i | − | 0.363626i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28360.4 | − | 42087.9i | 0.903602 | − | 1.34098i | ||||
\(996\) | −3024.69 | −0.0962260 | ||||||||
\(997\) | − | 10052.7i | − | 0.319329i | −0.987171 | − | 0.159664i | \(-0.948959\pi\) | ||
0.987171 | − | 0.159664i | \(-0.0510412\pi\) | |||||||
\(998\) | − | 24196.3i | − | 0.767457i | ||||||
\(999\) | −13088.9 | −0.414528 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 490.4.c.f.99.5 | 12 | ||
5.2 | odd | 4 | 2450.4.a.cy.1.5 | 6 | |||
5.3 | odd | 4 | 2450.4.a.cv.1.2 | 6 | |||
5.4 | even | 2 | inner | 490.4.c.f.99.8 | 12 | ||
7.2 | even | 3 | 70.4.i.a.39.2 | yes | 24 | ||
7.4 | even | 3 | 70.4.i.a.9.11 | yes | 24 | ||
7.6 | odd | 2 | 490.4.c.e.99.2 | 12 | |||
35.2 | odd | 12 | 350.4.e.n.151.2 | 12 | |||
35.4 | even | 6 | 70.4.i.a.9.2 | ✓ | 24 | ||
35.9 | even | 6 | 70.4.i.a.39.11 | yes | 24 | ||
35.13 | even | 4 | 2450.4.a.cw.1.5 | 6 | |||
35.18 | odd | 12 | 350.4.e.o.51.5 | 12 | |||
35.23 | odd | 12 | 350.4.e.o.151.5 | 12 | |||
35.27 | even | 4 | 2450.4.a.cx.1.2 | 6 | |||
35.32 | odd | 12 | 350.4.e.n.51.2 | 12 | |||
35.34 | odd | 2 | 490.4.c.e.99.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.i.a.9.2 | ✓ | 24 | 35.4 | even | 6 | ||
70.4.i.a.9.11 | yes | 24 | 7.4 | even | 3 | ||
70.4.i.a.39.2 | yes | 24 | 7.2 | even | 3 | ||
70.4.i.a.39.11 | yes | 24 | 35.9 | even | 6 | ||
350.4.e.n.51.2 | 12 | 35.32 | odd | 12 | |||
350.4.e.n.151.2 | 12 | 35.2 | odd | 12 | |||
350.4.e.o.51.5 | 12 | 35.18 | odd | 12 | |||
350.4.e.o.151.5 | 12 | 35.23 | odd | 12 | |||
490.4.c.e.99.2 | 12 | 7.6 | odd | 2 | |||
490.4.c.e.99.11 | 12 | 35.34 | odd | 2 | |||
490.4.c.f.99.5 | 12 | 1.1 | even | 1 | trivial | ||
490.4.c.f.99.8 | 12 | 5.4 | even | 2 | inner | ||
2450.4.a.cv.1.2 | 6 | 5.3 | odd | 4 | |||
2450.4.a.cw.1.5 | 6 | 35.13 | even | 4 | |||
2450.4.a.cx.1.2 | 6 | 35.27 | even | 4 | |||
2450.4.a.cy.1.5 | 6 | 5.2 | odd | 4 |